دانلود کتاب تئوری و تحلیل مجموعه A.P. مورس

My purpose in putting this book together is to make more people aware of the work of A. P. Morse in regard to his development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. This text is primarily a combination of Morse’s book A Theory of Sets, Second Edition (1986) and notes for a course on analysis from the early 1950’s. It has been supplemented and updated with subsequent course notes and publications of Morse. Morse provided very little in the way of explanation in his written work. I believe that he thought the careful statements in formal or nearly formal language should speak for themselves. This creates a formidable challenge for those who would try to read his work. As an aid and guide to readers, I have tried to provide some commentary and insight in the Editor’s Introduction. This book is based on both previously published material and unpublished notes, and therefore would not be possible without several permissions. I am grateful to Elsevier Publications for granting me permission to republish the material, slightly altered, from A Theory of Sets, Second Edition (1986). Likewise I am grateful to the American Mathematical Society for allowing me to reproduce material from Web Derivatives (1973). I am especially thankful for the permission and support shown by the families of Tony Morse and Hewitt Kenyon, in particular Peter Morse and Linda and Emily Kenyon. I am grateful to Robert Arnold for allowing me to use material from his Ph.D. thesis Plus and Times (1969). I wish to thank Douglas Bridges for suggesting the comparison of Morse’s integral to the Henstock- Kurzweil integral. In 1966, Bob Neveln, my friend since junior high school, had taken a year’s leave of absence from his undergraduate studies at Caltech to spend a year at Northwestern University where I was attending school. During that period he bought A Theory of Sets (1965) and showed it to me. We began studying Morse’s work then, and have never looked back. Bob has encouraged me during the years I worked on this project, and has used a parser he developed to check the correctness of the formal syntax.